**The Mathematics of Book Making**

In the gambling vernacular, making a book is the procedure of laying wagers on the numerous possible results of an event. The term stems from the original system for recording bets before the wonderful ease of electronics: wagers were noted in a ledger, or book, and the person recording these, or making the book, became known as the bookmaker. The mathematics of book making is a subject of close study for those who are involved in the world of gambling, as it allows them to predict the outcomes for the events available for betting with far more accuracy.

The mathematics of book making allow bookmakers to offer bets on the outcome of a particular event that is made up of the right proportions so that he or she is able to see a profit no matter which result ends up occurring. This is largely achieved by regulating what are established as the true odds of the different results of an event in a downward fashion. This means that the bookmaker will only make payouts using his or her actual odds, and the amount held to be less than the true odds would be paid out, this making certain that a profit is made.

**Fixed and Fluctuating Odds Provided**

Although the odds provided for a specific event may well be fixed, the mathematics of book making would preferably have them fluctuating, with this characteristic taking the size of bets made before the event begins into account.

When it comes to the mathematics of book making it is vital to comprehend the connection between relative probabilities and odds. If a football match is taken as an example there are three possible outcomes:

- A home win.
- A draw.
- An away win.

The mathematics of book making has these odds, which may be met in order to properly represent the true chance of these three outcomes:

- Evens for a home win.
- Two to one for a draw.
- Five to one for an away win.

When these odds are displayed as percentages, by multiplying them by 100, the likelihood of each result can be more thoroughly understood:

- There is a one to one chance of a home win, thus a 50% chance that this result will occur.
- There is a two to one chance of a draw, thus the likelihood of this outcome is 3%.
- There is a five to one chance of an away win, so the probability of this outcome prevailing is 3%.

The mathematics of book making has the bookmaker adding these percentages together in order to achieve a total of 100%, with this number representing a fair book. In order to ensure his or her profit, the bookmaker will always reduce these odds. The example above thus becomes:

- A four to six chance of a home win, or 60% probability.
- A six to four chance of a draw, or 40% probability.
- A four to one chance of an away win, or 20% probability.